In general, this looping problem is due to the fact that your account believes you've previously had an authenticator app installed, which commonly occurs when a smartphone is either lost or replaced with a new phone without restoring the backup.
Since you don't indicate whether this is truly your first installation or a replacement, I'll simply state that you should likely login using other verification methods like password, alternate phone (text) or email and then use the Security, Advanced security options to remove any existing 'Send sign-in notification' item, since this is where any existing authenticator information is stored.
Of course, if you had a previous authenticator working and the replacement is simply due to a new phone, it might be best to try and recover the backup from your account if that was ever created, since it will contain not only your Microsoft, but also any other 3rd-party username/password and/or TOTP code information previously stored in the backed-up app.
Back up and recover account credentials in the Authenticator app - Microsoft Support
Since these instructions are related to a Microsoft Personal account typically used by wither consumers or very small businesses with a single user, the instructions are different for Work or School accounts, since those typically have IT support administrator or help desk operations who perform some of these duties for their users instead. In that case, you should be contacting those support individuals, but if you happen to be a small business with an Azure account where you're also the administrator, though the issue and solution are similar, the precise method(s) used to remove and reconfigure a Microsoft Authenticator app are different based on the product and the management interface used to manage it. Contacting whateve3r Microsoft Support group specifically supports the product you're using is the best path to take in these cases where no local IT support actually exists.
Rob